The Obama administration and Russia have been at odds as of late over a number of issues, including whistleblower Edward Snowden's asylum, the civil war in Syria, Russia's treatment of gay people and, more recently, the conflict in Ukraine.

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Some pundits have speculated that Putin is using the disagreements to escalate diplomatic tensions into a second Cold War between the two superpowers, but Rice reiterated the Obama administration's opposition to any such conflict.

"We have confronted him, and we do call him on it. The president is very plain and very forceful in his dealings with Putin," Rice told NBC's "Meet the Press." "But it's not necessary, nor is it in our interest, to return to a Cold War construct, which is long out of date and that doesn't reflect the realities of the 21st century."

The conflict in Ukraine is the latest example of rising tensions between the U.S. and Russia. Rice suggested that she wouldn't be surprised if Putin views the disagreements from a Cold War perspective, even if the Obama administration doesn't.

"He may, but if he does, that's a pretty dated perspective that doesn't reflect where the people of Ukraine are coming from," Rice said. "This is not about the U.S. and Russia. This is about whether the people of Ukraine have the opportunity to fulfill their aspirations and be democratic and be part of Europe, which they choose to be."